Two approaches to determine public good provision under distortionary taxation.

INTRODUCTION

The overall aim of the present paper is to discuss the role of tax regimes and the optimality of tax policy for the assessment of public projects, and to shed light on previous contributions from this perspective. Despite being a long-standing and central issue in public finance, the issue of what is the most appropriate approach to determine the provision level of public goods financed by taxes appears to be an unresolved one. While for many years the famous Samuelson rule (Samuelson, 1954) was the prevailing guide to public good provision, recognition of inevitable tax distortions has added considerable complexity. The standard argument is that taxes levied to finance public goods will inflict a loss of efficiency on society by inducing behavioral responses that are socially inefficient, even if privately rational. This is a social cost that must be added to the cost in terms of resources needed to produce the public good. A popular statement is that the tax payers will incur a loss of private income that exceeds the revenue raised by the tax collector. There is a marginal cost of public funds exceeding unity. (1) This story can be extended and modified along several dimensions. Firstly, it has been noted that the provision of public goods may itself induce behavioral responses that may alleviate, but could also aggravate, the tax distortions, as highlighted for instance in Atkinson and Stem (1974). (2) Secondly, it has been pointed out that it is inappropriate to neglect distributional effects as the reason why distortionary taxes are deployed in the first place is that redistribution is pursued subject to asymmetric information or other constraints that rule out person-specific lump-sum taxes.

The various arguments above have been nicely integrated in the cost-benefit approach of Slemrod and Yitzhaki (2001). This is based on four concepts, two on the cost side and two on the benefit side. On the cost side, a marginal efficiency cost of public funds (MECF) is defined as the aggregate loss of private income per unit of public revenue, and a distributional characteristic ([DC.sub.c]) is defined as the weighted average of the social evaluation of the marginal utility of income, weighted by the share of each individual in the burden of raising the tax revenue. On the benefit side, a marginal efficiency benefit of the public project (MEBP) is defined as the monetary value to the individuals per additional dollar spent by the government, and a distributional characteristic ([DC.sub.b]) is defined as the welfare-weighted average of the individuals' shares in the total benefit. The cost-benefit rule requires that [DC.sub.c] x MECF be equated to [DC.sub.b] x MEBP. (3)

While there is a lot to be said for this elegant social welfare approach, its disadvantage is that it requires access to a detailed social welfare assessment. Beyond the knowledge required by the Samuelson rule and information on behavioral responses, there is a need to know the social welfare weights to be assigned to the respective agents. The latter is information that is not readily available to the cost-benefit analysts. In this paper I want to argue, in the spirit of the Samuelson rule, that the Pareto efficiency criterion in many cases should be considered as an alternative to the Slemrod and Yaitzhaki (2001) approach to determine the public good provision. Which approach is the more appropriate one should be determined by the available tax regime. I will distinguish between "rich" tax regimes, which are capable of preserving the utility levels of all groups when there is an increase in the public provision (permitting any change in tax revenue), (4) and "restrictive" tax regimes, which are not. (5) The key argument is that when a rich tax regime is available, the cost-benefit analyst can appeal to the Pareto-principle, as does the Samuelson rule, rather than a social welfare objective.

As there may be many Pareto efficient allocations, Pareto efficiency conditions are in general inadequate to determine public good provision, unlike the social welfare approach, which ideally embraces all relevant social welfare concerns. However, the perception of the government as a single entity simultaneously in full command of all policy instruments, aware of all relevant constraints, and taking all aspects of social welfare into account is not entirely appealing. In practice it is hard to dismiss the idea that there should be some division of labor between branches of government being respectively in charge of the "allocation function" and "distribution function" of government in the terminology of Musgrave (see Musgrave and Musgrave (1973)). I will pursue this idea further below.

In the following, and in line with most of the previous literature in this field, I will consider projects that are sufficiently small to be analyzed by first order effects.

The paper proceeds as follows. The next section will elaborate on the Pareto approach. The subsequent section will review the Slemrod and Yitzhaki (2001) approach to public good provision under the simple regime of a linear income tax. I then address the Pareto approach within the linear income tax model, and contrast the two approaches before extending the discussion to a non-linear income tax. A separate section is devoted to the role of optimum taxation, which has been an obscure issue in the literature on the assessment of public projects. Finally, I establish links to related literature, and offer some concluding remarks.

THE SCOPE FOR PARETO IMPROVEMENTS

Suppose that the tax system is rich enough to allow the policy maker to keep everybody at an unchanged utility level when there is a change in the public good provision. Assuming that everybody derives a non-negative utility from the additional provision, an offsetting extra tax burden would be imposed on every agent. More tax revenue would be collected and the net revenue would increase or not depending on whether the tax proceeds exceed the additional expenditure on public goods. Attaining a surplus is clearly a sufficient and necessary condition for a Pareto improvement as a surplus can be recycled to some or all agents, while a deficit would make it necessary to impose an extra burden (beyond the utility-preserving extent) on at least some agent(s).

If, under a rich tax regime, no Pareto improvement is possible, a welfare improvement might still be feasible but would require a socially favorable redistribution. As, with Pareto improvements precluded, a project would generate a net revenue deficit at constant utilities, we might alternatively assume that the project in the first place is fully funded by tax changes making nobody better off, and some worse off. Then obviously a socially favorable, pure redistribution would be needed to generate a welfare improvement. Such redistribution would not have to rely on any public project, and should not be allowed to interfere with any project appraisal. If, under a rich tax regime, a project cannot yield a Pareto improvement, it should be rejected.

The most prominent example of a rich tax regime is obviously the unrestricted lump-sum taxes underlying the Samuelson rule. Any change in individual utility due to a public project can be offset by adjusting individualized lump--sum taxes, and a revenue surplus is generated unless the Samuelson rule is already valid. With restrictions on individualized lump-sum taxes, say only a uniform lump-sum tax (poll tax) is available, this will no longer hold true. More realistically, we can imagine that a proportional income tax is the only available tax instrument to finance a public good enjoyed by a heterogeneous population. Then there is a unique relationship between the amount of the public good and the tax rate, possibly after ignoring a downward-sloping portion of a humped-shaped Laffer curve that can be dismissed as Pareto inferior. Such a tax regime will seriously restrict, if not entirely eliminate, the scope for Pareto improvements. If the marginal valuation of the public good is either sufficiently steeply or modestly increasing in income, an increase in the tax and public provision level will benefit some individuals at the expense of others. Then a welfare comparison will have to be made to determine whether "large" benefits (losses) for the rich outweigh "small" losses (benefits) for the poor. Even if the Pareto criterion might still rule out certain allocations, say because a tax increase from a very low level might make everybody better off, it provides a very limited and not very helpful guide to public good provision under such restrictive regimes.

The advantage of being able to trace Pareto improvements is that there is no need to determine social welfare weights in order to accept a project. We can conceive of the allocation branch as an agency in charge of eliminating deviations from Pareto efficiency by carrying out Pareto improvements whenever feasible. (6) It may solely decide whether the public project should be carried out, leaving to the distribution branch to determine the tax changes to fund it. Or, in other words, if we think of the allocation branch as adjusting taxes to maintain the utility of all agents, it will be the task of the distribution branch to recycle any revenue surplus.